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Mean-Value Theorem for Integrals

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Presentation on theme: "Mean-Value Theorem for Integrals"— Presentation transcript:

1 Mean-Value Theorem for Integrals
AP Calculus Ms. Olifer

2 Mean Value for Integrals
b c If f(x) is continuous on the closed interval [a, b], then there exists a number c in the closed interval [a, b] such that

3 Mean Value for Integrals
Since We can solve for The theorem does not give us the value of c How can we find it?

4 Given f(x) = x2 + 4x + 1 on [0,2]. Find the value of c so that

5 Average value of a function
The average value of function f on the interval [a, b] is defined as Example: Find the average value of f(x)=x3 on [0,2].

6 Example Find the average value of on the interval [0.5, 2]

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